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A few concepts: electric force, field and potential Gravitational Force –What is the force on a mass produced by other masses? – Kepler’s Laws & Circular Motion Gravitational Potential Energy – Conservation of Energy Electric force: –What is the force on a charge produced by other charges? –What is the force on a charge when immersed in an electric field? Electric field: –What is the electric field produced by a system of charges? (Several point charges, or a continuous distribution)

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Plus a few other items… Electric field lines Electric dipoles: field and potential produced BY a dipole, torque ON a dipole by an electric field, torque and potential energy of a dipole

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Conservation of Mechanical Energy!

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Kepler’s Laws and Orbitronics for Circular Motion

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Charged Insulators & Conductors Will two charged objects attract or repel? Can a charged object attract or repel an uncharged object?

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Electric forces and fields: point charges Figure 22N-14 shows an arrangement of four charged particles, with angle  = 34° and distance d = 2.20 cm. The two negatively charged particles on the y axis are electrons that are fixed in place; the particle at the right has a charge q 2 = +5e (a)Find distance D such that the net force on the particle at the left, due to the three other particles, is zero. (b) If the two electrons were moved further from the x axis, would the required value of D be greater than, less than, or the same as in part (a)? Other possible questions: what’s the electric field produced by the charges XXX at point PPP ? what’s the electric potential produced by the charges XXX at point PPP ? What’s the potential energy of this system?

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Electric dipoles What’s the electric field at the center of the dipole? On axis? On the bisector? far away? What is the force on a dipole in a uniform field? What is the torque on a dipole in a uniform field? What is the potential energy of a dipole in a uniform field?

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Electric fields of distributed charges Possible problems, questions: What’s the electric field at the center of a charged circle? What’s the electric field at the center of ¼ of a charged circle? What’s the electric field far from the ring? far from the disk? What’s the DIRECTION of an electric field of an infinite disk?

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Exam Review Continued Questions: from checkpoints and questions in the textbook!

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Problem Calculate electric field at point P. P x L a dx E Field very far away?

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Problem Field at center of arc?

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Line Of Charge: Field on bisector Distance Charge per unit length Q L a P o x dE dx d

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Line Of Charge: Field on bisector What is E very far away from the line (L<> a)?

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Electric fields: Example Calculate the magnitude and direction of the electric field produced by a ring of charge Q and radius R, at a distance z on its axis.

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Sample Problem Figure 22N-14 shows an arrangement of four charged particles, with angle  = 34° and distance d = 2.20 cm. The two negatively charged particles on the y axis are electrons that are fixed in place; the particle at the right has a charge q 2 = +5e (a)Find distance D such that the net force on the particle at the left, due to the three other particles, is zero. (b) If the two electrons were moved further from the x axis, would the required value of D be greater than, less than, or the same as in part (a)?